Amount of light that come out of a luminaire is called lumen. Thus lumen could be defined as a measurement of light emitted from source ( LM ). Thus the higher value of LM means a higher value of light brightness.
On the other hand lux is related to lumen as it is defined as measurement of amount of light per unit area m2. The need of lux may come up once comparison between light sources intensity over specific area is needed. Thus better light type could be chosen. While watt is related to the amount of energy consumed from lighting sources.
As a conclusion higher light intensity over a specific area means higher lux which means higher lumen received, but this does not mean in need a higher watt is consumed. As some types of new lighting systems like LED gives higher LM/m2 with lower watt consumption than older lighting ones.
